关于具有非连续权重采样的随机基展开中通用逼近的高概率性
On high probability of universal approximation in random basis expansions with non-continuous weight sampling
AI总结：
研究随机基展开的通用逼近性质，将其从连续权重采样和实值激活函数扩展到非连续权重分布及复值激活函数，证明此类随机基具有任意高概率的通用逼近性质。
AI中文摘要：
随机基展开（RBE）通过随机采样基的跨度来寻找目标函数的最佳逼近，等同于隐藏层权重随机选择的单层神经网络。已利用连续权重采样分布和实值激活函数建立了RBE的通用逼近性质。本文结果将通用逼近性质扩展到使用权重空间中具有密集支撑的非连续权重分布以及复值激活函数的RBE，表明此类随机基具有任意高概率的通用逼近性质。
英文摘要：
Random basis expansion (RBE) search the span of a randomly sampled basis to find the best approximation of a target function. They are equivalent to single layer neural networks where the hidden layer weights are chosen randomly. Universal approximation properties have been established for RBEs using continuous weight sampling distributions and real-valued activation functions. Our results extend the universal approximation property to RBEs that use non-continuous weight distributions with dense support in the weight space and that use complex-valued activation functions. The result shows such random bases have the universal approximation property with arbitrarily high probability.
